Problem: Solve for $x$ and $y$ using elimination. ${-3x-3y = -45}$ ${-4x+2y = -24}$
Solution: We can eliminate $y$ by adding the equations together when the $y$ coefficients have opposite signs. Multiply the top equation by $2$ and the bottom equation by $3$ ${-6x-6y = -90}$ $-12x+6y = -72$ Add the top and bottom equations together. $-18x = -162$ $\dfrac{-18x}{{-18}} = \dfrac{-162}{{-18}}$ ${x = 9}$ Now that you know ${x = 9}$ , plug it back into $\thinspace {-3x-3y = -45}\thinspace$ to find $y$ ${-3}{(9)}{ - 3y = -45}$ $-27-3y = -45$ $-27{+27} - 3y = -45{+27}$ $-3y = -18$ $\dfrac{-3y}{{-3}} = \dfrac{-18}{{-3}}$ ${y = 6}$ You can also plug ${x = 9}$ into $\thinspace {-4x+2y = -24}\thinspace$ and get the same answer for $y$ : ${-4}{(9)}{ + 2y = -24}$ ${y = 6}$